Long time behavior for a semilinear hyperbolic equation with asymptotically vanishing damping term and convex potential

DOI10.1016/j.jmaa.2015.04.067zbMath1316.35036arXiv1412.7008OpenAlexW2963074050MaRDI QIDQ2348425

Ramzi May

Publication date: 12 June 2015

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.7008

zbMATH Keywords

energy functiondissipative hyperbolic equationasymptotically small dissipation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Abstract hyperbolic equations (35L90) Second-order semilinear hyperbolic equations (35L71)

Related Items (10)

Inertial primal-dual dynamics with damping and scaling for linearly constrained convex optimization problems ⋮ Optimal decay rates for semi-linear non-autonomous evolution equations with vanishing damping ⋮ Asymptotic stability of intermittently damped semi-linear hyperbolic-type equations ⋮ Asymptotic for a second-order evolution equation with convex potential andvanishing damping term ⋮ Unnamed Item ⋮ Asymptotic for the perturbed heavy ball system with vanishing damping term ⋮ Convergence Rates of Inertial Primal-Dual Dynamical Methods for Separable Convex Optimization Problems ⋮ Decay rates for second order evolution equations in Hilbert spaces with nonlinear time-dependent damping ⋮ Optimal energy decay rates for abstract second order evolution equations with non-autonomous damping ⋮ Stability for nonlinear wave motions damped by time-dependent frictions

Cites Work

• Asymptotics for some semilinear hyperbolic equations with non-autonomous damping
• Convergence of global and bounded solutions of a second order gradient like system with nonlinear dissipation and analytic nonlinearity
• Convergence of solutions to second-order gradient-like systems with analytic nonlinearities
• Asymptotics for a second order differential equation with a linear, slowly time-decaying damping term
• On the Long Time Behavior of Second Order Differential Equations with Asymptotically Small Dissipation
• On the long time behavior of second order differential equations with asymptotically small dissipation
• On the Minimizing Property of a Second Order Dissipative System in Hilbert Spaces
• Asymptotics for a second-order differential equation with nonautonomous damping and an integrable source term
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Unnamed Item

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